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How many terms of the series are needed in order to estimate the exact sum within .01

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    How many terms of the series

    Ʃ (-1)n/(ln(n+1))
    n=1
    are needed in order to estimate the exact sum within .01
    2. Relevant equations

    I know that I need to use the remainder estimate for the integral test where Rn=s-sn

    and that ∫ from (n+1) to ∞ of f(x)dx [itex]\leq[/itex] Rn [itex]\leq[/itex] ∫ from (n) to ∞ of f(x)dx



    3. The attempt at a solution

    I tried to take the integral but I don't know how, and I cant figure out another way to approach the problem
     
  2. jcsd
  3. Nov 6, 2011 #2

    LCKurtz

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    Gold Member

    Re: How many terms of the series are needed in order to estimate the exact sum within

    I don't think you want to use an integral.

    Hint: Don't you have a theorem for alternating series (with certain hypotheses) that compares the error to the first term not included?
     
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